Similar methods have been generalized to fit sparse data in the multivariate functional setting. Still, the depth of sparse multivariate functional data has not been considered in detail. [1]} ([1]}) modeled paired longitudinal data with principal components and fitted them by penalized splines under the mixed-effects model framework. However, their method is limited to only two variables when the data are either observed or missing simultaneously. [3]} ([3]}) proposed a multivariate functional principal component analysis defined on different time grids, which is also suitable for data with missing values. [5]} ([5]}) derived a fast algorithm for fitting sparse multivariate functional data via estimating the multivariate covariance function with tensor product B-spline. The limited discussion of possible depths for sparse multivariate functional data gives us much space to explore before providing the ranks for data visualization.
